There has been no attention to circular (purely cyclical) data in political science research. We show that such data exists and is generally mishandled by models that do not take into account the inherently recycling nature of some phenomenon. Clock and calendar effects are the obvious cases, but directional data exists as well. We develop a modeling framework based on the von Mises distribution and apply it to two datasets: casualties in the second Iraq war and party movement in a two-dimensional ideological space. Results clearly demonstrate the importance of circular regression models to handle periodic and directional data.